The lab today was amazing. My AP Physics C students from last year set up these hidden circuits for each other. They had five or six resistors in them, and they tucked all the wires inside an overturned box so that only the resistor and the tips of the wires attached to the resistor poked out of holes in the box. They were difficult and students used a lot Kirchhoff's Law to figure out the underlying circuit structure when they could only measure voltage across and current through the resistors. I had them simplify the circuits so there were only three resistors. Those I kept, with the schematic diagrams they drew, until today.
I put them in groups of 5 groups of 4 around the 5 different circuits in the room. They together tried to figure out how the three resistors would hooked up in the circuit. Then I told them the four people in their group had to scatter to four different tables, and we did a second round. And then the third round.
And then the insight happened. Instead of just showing them the answer keys, we would make the answer keys. Those students who analyze the circuit in lab had to go to the front of the board and discuss how they think the circuits were wired. Those who never got to see that particular setup took it apart and, from the jumble of wires, tried to figure out how it was set up. Those students also used the ohmmeter function of the multimeter to find the resistance of the resistors in the circuit.
This was great. The students argued in the front of the room. I taught the students in the back how to use the ohmmeter and how to look at a tangle of wires and draw an ideal circuit.
The most discussion happened in the circuit where all the resistors had the same voltage drop but where the current in one resistor equaled the sum of the currents in the other two resistors.
At the beginning of class, we whiteboarded some problems, and I took pictures of them, but I'm not even including them. The lab after was better.